Chemistry by numbersor: How I learned to stop worryingand love computational chemistry.

James C. Womack

University of Bristol

04 July 2012

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Outline

I Computational chemistry.

I Method development.

I My own research.

Photo: “Red Onion Slice” by photobunny (Flickr)

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What is computational chemistry?

Using computers to study chemistry!

I Many different approaches, e.g. informatics, simulation.

Theoretical chemistry: “the subfield [of chemistry] wheremathematical methods are combined with fundamental laws ofphysics to study processes of chemical relevance” [1].

Quantum chemistry:

ElectronsNucleiConstantsEnvironment

OrbitalsEnergyStructure

ThermochemistrySpectral propertiesReactivity

Theory

Wavefunction

Ψ

[1] Jensen, F. Introduction to Computational Chemistry. (Wiley: 2007), pp. 1.

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Why use computational chemistry?In place of lab work:

I Eliminate the unprofitable or irrelevant.I e.g. virtual screening of drug candidates [1].

I Some systems inaccessible to experiment.I e.g. astrochemistry [2], radioactive decay [3].

time

1 2 3 4 5 6

α

U

[1] Schneider, G., Nature Reviews Drug Discovery 9, 273 - 276 (2010).

[2] Woon, D. E. & Herbst, E., The Astrophysical Journal Supplement Series 185, 273 - 288 (2009).

[3] Archer, A., Allan, N. L., ongoing research, University of Bristol, Centre for Computational Chemistry.

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Why use computational chemistry?To enhance understanding and gain new insights:

I Inspire and inform new research.I Can “play” with a system easily.I Facilitate rational design of approaches and products.

I e.g. drug design (raltegravir) [1]

I e.g. catalyst design (Mannich) [2]

[1] Schames, J. R., McCammon, J. A., et al., J. Med. Chem. 47, 1879 - 1881 (2004).

[2] Mitsumori, S. et al., J. Am. Chem. Soc. 128, 1040 - 1041 (2006).

Raltegravir structure: Croxtall, J. D. & Keam, S. J. Raltegravir. Drugs 69, 1059 - 1075 (2009).

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Method development: faster, better science

Motivations:

I Faster calculations.

I Greater accuracy.

I New systems and situations.

I Improved practicality /accuracy compromise.

. . . more science per Watt!

Image: BlueCrystal supercomputer, University of Bristol.

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Method development: example

Accurate enzyme reaction barriers with QM/MM methods [1].

[1] Claeyssens, F. et al., Angewandte Chemie International Edition 45, 6856 - 6859 (2006).

Image: Hen egg-white lysozyme in solvent (Mike Limb, University of Bristol).

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Method development: example

Modelling the QM region:

I Semi-empirical methods, error ≈10 kcal mol−1.

I DFT underesimates barrier heights (several kcal mol−1).

I Higher level methods accurate but too expensive.

I Local methods allow high level calculations at lower expense.

Method CM PHBHDFT 10.2 8.4Local CCSD(T0) 13.1 13.3Experiment 12.7 12.0

Averaged activation enthalpies (300K), kcal mol−1

Improved accuracy allows. . .“quantitative studies of reaction mechanisms in enzymes”.

[1] Claeyssens, F. et al., Angewandte Chemie International Edition 45, 6856 - 6859 (2006).

Table adapted from [1]. CM = chorismate mutase, PHBH = para-hydroxybenzoate hydroxylase.

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My research: electron correlation

Quantum chemistry: find E by solving HΨ = EΨ

Electron-electron correlation isimportant to describe chemistry!

I Bond dissociation.

I Dispersion interactions.

. . . important for accurate E. +

e1

e2

(x1,y1,z1)

(x2,y2,z2)

Conventional wavefunction, Ψ, based methods:I Electron coordinates are independent.

I Inefficient for describing correlation.I Poor scaling of cost with error in correlation energy.

I Reducing the error by a factor of 10 requires a 10000-foldincrease in computer time [1].

[1] Klopper, W., Manby, F. R., Ten-No, S. & Valeev, E. F., International Reviews in Physical Chemistry 25,427 (2006).

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My research: explicitly-correlated methods

Explicitly correlated methods:

I Electron coordinates are notindependent.

I Electron correlation “builtin” to wavefunction.

I Improved scaling of costwith error in correlationenergy.

+

e1

e2

(x1,y1,z1)

(x2,y2,z2)

r12

BUT: Many-electron integrals arise:

I All methods require 1- and 2-electron integrals.

I Many-electron integrals are costly and numerous.

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My research: approximating integralsCurrent widely used method: resolution of the identity (RI) [1]

〈ijm|f12f23|mkl〉 ≈∑p

〈ij|f12|mp〉〈pm|f23|kl〉

O(N6), 3locc [2]

Alternative method: density fitted orbital pairs [3]

(im|f12|jk|f23|ml) ≈∑

A,B,C

DimA Djk

B DmlC (A|f12|B|f23|C)

O(N5), 2locc [2]

[1] Kutzelnigg, W. & Klopper, W., J. Chem. Phys. 94, 1985 (1991).

[2] Manby, F.R. Explicitly correlated electronic structure theory. Solving the Schrodinger equation: haseverything been tried? (2011), ed. Paul Popelier, Imperial College Press.

[3] Manby, F.R., J. Chem. Phys. 119, 4607 (2003).

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My research: implementation

I Derive many-electron integrals without RIs.

I Derive approximate density-fitted forms of the integrals.

I Write code to generate the integrals in Molpro [1].

I Run calculations using the new integral approximation.

I Compare against existing methods.

[1] MOLPRO, a package of ab initio programs, H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M.Schutz, and others , see http://www.molpro.net.

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Acknowledgements

I would like to thank the following people and organizations:

I Prof Fred Manby

I Prof Neil Allan

I Prof Adrian Mulholland

I Dr Natalie Fey

I Colleagues at the Centre for Computational Chemistry.

I SCI College of Scholars

I EPSRC

I University of Bristol

Appendix: Activation enthalpies (300K) (kcalmol−1)

Method CM PHBHHartree-Fock 28.3 (2.1) 36.7 (2.6)B3LYP 10.2 (1.8) 8.4 (1.4)LMP2 9.5 (1.0) 10.7 (1.2)LCCSD(T0) 13.1 (1.1) 13.3 (1.5)Experiment 12.7 12.0

Activation enthalpies from averages of energy differences from single-point QM/MM

calculations for the reactant complex and the TS on different adiabatic pathways.

aug-cc-pVTZ basis used on oxygen and cc-pVTZ on all other atoms; point-charge

representation of the MM environment was included in the QM calculations

CM = chorismate mutase, PHBH = para-hydroxybenzoate hydroxylase

Table adapted from slide provided by A. J. Mulholland, University of Bristol

Claeyssens, F. et al., Angewandte Chemie International Edition 45, 6856 - 6859 (2006).

Appendix: Computational science at Bristol

I BlueCrystal:I 66 in top 500 in 2008.I 3360 2.6 GHz x86

processor cores.I Some GPGPU and large

memory nodes.I >600 users across the

university.

I Uses for chemistry:I Docking simulations.I Molecular dynamics.I Climate modelling.I Quantum chemistry.I Reaction dynamics.

BlueCrystal information and image: Dr Ian Stewart, Director of Advanced Computing, University of Bristol.